Cardiac output (CO) is defined to be the volume of blood ejected by the heart per a unit time. Since CO also represents the total flow of blood supplying all the tissue beds of the body, it is perhaps the most indicative quantity of the state of the heart and circulation. CO is routinely measured in intensive care units and surgical suites in order to monitor and guide therapy for critically ill patients. These patients include, for example, those in shock (e.g., cardiogenic, hemorrhagic, or septic) or heart failure and those during and after surgery (e.g., coronary artery bypass grafting or heart valve replacement.)
An ideal CO measurement technique would be simple to perform, inexpensive, noninvasive or minimally invasive and safe, and very accurate. However, none of the conventional measurement techniques known in the art possess all of these characteristics [10]. For example, the thermodilution technique, which is currently employed in most intensive care units and surgical suites, involves injecting cold saline into the right atrium and measuring the temperature downstream in the pulmonary artery. The average CO over the measurement period may than be computed from conservation of mass laws. Although the technique is relatively simple and inexpensive, it requires an invasive right heart catheterization whose safety is questionable [8,38] and is not very accurate due to the many assumptions upon which it is based (e.g., no saline recirculation and thorough blood mixing) [10,27]. The most accurate, conventional technique for measuring CO involves surgically implanting a flow probe, either electromagnetic or ultrasonic, directly on the aorta. Although this technique also provides a continuous measurement of CO, it requires a high risk thoracotomy which is rarely performed in practice. Moreover, the accuracy of the aortic flow probe is highly dependent on vessel preparation and may only be accurate to within about 15-20 percent [10,27].
Although the development of an ideal CO measurement technique has proven to be difficult, several ideal, or near ideal, techniques are currently available for the continuous measurement of peripheral arterial blood pressure such as Finapres technology [23] and arterial tonometry [25]. Previous investigators have therefore sought techniques to monitor CO from peripheral arterial blood pressure signals. The most popular techniques in the art are the so-called pulse contour methods that assume the arterial tree to be well represented by a parallel combination of a capacitor and resistor thereby accounting for the compliance of the large arteries (AC) and the total peripheral resistance (TPR) of the small arteries. If the instantaneous CO supplied by the heart is represented as a current source, then the simple model of the heart and arterial tree in FIG. 1A results. Most of these types of pulse contour methods are specifically based on mathematical formulas which are derived by making simplifying assumptions and approximations to this model (see, for example, [7, 19-21, 26, 40, 43, 44]). These methods have generally failed to yield good correlation between CO determined from analysis of ABP signals and directly measured CO over a wide range of physiologic conditions [39, 42].
Bourgeois et al. [3,4] did successfully demonstrate that their pulse contour method when applied to an ABP signal measured centrally in the aorta could yield a quantity which varied linearly with directly measured CO (electromagnetic aortic flow probe) over a wide range of physiologic conditions. Their method, which makes no simplifying assumptions or approximations to the model of FIG. 1A, may be explained as follows. During the diastolic period of each cardiac cycle, the heart is filling and not supplying blood to the arterial tree (see FIG. 1B). Thus, according to the model, ABP decays with a time constant τD equal to the product of TPR and AC during each diastolic period (see FIG. 1B). Since AC is essentially constant over a wide pressure range and on the time scale of days [4, 18,37], CO could then be monitored to within a constant scale factor (equal to the reciprocal of AC) by dividing the ABP by τD.
Bourgeois et al. specifically demonstrated that beat-to-beat CO may be monitored from τD and the governing differential equation of the model of FIG. 1A. Thus, a key step of the pulse contour method of Bourgeois et al. is to fit an exponential to the diastolic decay portion of an ABP wavelet in order to measure τD. Osborn et al. [34] introduced essentially the same method prior to Bourgeois et al. but their experimental validation was not as complete or compelling.
Bourgeois et al. were able to validate their pulse contour method with respect to a canine ABP signal measured centrally in the aorta, because the diastolic portion of such a signal usually resembles an exponential decay (see FIG. 2A). These investigators specifically identified the position in the aorta at the level of the dorsal insertion of the diaphragm as the optimal site for observing an exponential diastolic decay. However, Bourgeois et al. acknowledged that central ABP is rarely obtained clinically because of the difficulty in inserting a catheter retrogradely via a peripheral arterial blood vessel and the risk of blood clot formation and embolization. Moreover, they recognized that, in peripheral ABP signals which are routinely made available in intensive care units and surgical suites usually via a more simple and safe radial artery catheterization, an exponential diastolic decay is usually not apparent (see FIG. 2B). The method of Bourgeois et al. therefore cannot generally be applied to readily available peripheral ABP signals. In fact, its application to central ABP signals may be somewhat limited, as Cundick et al. [9] reported that they could not identify an optimal location in the human aorta in which the diastolic portion of the ABP signal appeared as a pure exponential decay.
Other pulse contour methods that are based on more complex representations of the arterial tree have also been developed (see, for example, [5, 11, 12, 16, 24, 31-33, 50]). However, these techniques required the analysis of one, or even two, central ABP signals. Thus, their clinical utility is also severely limited.
Several techniques have more recently been introduced in an attempt to monitor CO from ABP signals measured peripherally. Techniques based on an adaptive aorta model which require ABP signals measured at two peripheral sites—the carotid artery and the femoral artery—have been developed [36, 46]. However, catheters are usually not placed for prolonged periods of time at either of these sites in intensive care units or surgical suites due to issues of safety. Another previous technique is based on an empirically-derived formula which involves the calculation of the derivative of the ABP signal [14]. However, in order to mitigate the corruptive effects of wave reflections on the derivative calculation, this technique also requires two peripheral ABP measurements, one of which is obtained from the femoral artery. Other techniques based on a learning approach have been previously proposed [6, 15, 30]. However, these techniques require extremely large sets of training data consisting of simultaneous measurements of CO and ABP signals obtained over the entire range of physiologic conditions. Moreover, the success of these techniques was only demonstrated with central ABP signals or only over a narrow physiologic range. Finally, Wesseling et al. [1, 48, 49] and Linton and Linton [28] have recently proposed model-based techniques which require only the analysis of a single radial artery pressure signal. However, Linton and Linton showed that their technique was reasonably accurate only over a narrow range of physiologic conditions, and several previous studies have demonstrated the inadequacy of the method of Wesseling et al. (see, for example, [13, 22]).
It is evident that there remains a need in the art for methods and apparatus for determining CO reliably and accurately using information obtained from the arterial blood pressure signal. In particular, there remains a need in the art for methods and apparatus for determining CO reliably and accurately using information obtained from the peripheral arterial blood pressure signal.